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Two techniques for discretization of 3D models described in terms of boundary representation of free-form model entities have been presented.

The first one is based on advancing front technique in sequential environment. The octree data structure is used to control the mesh gradation and to efficiently perform spatial localization. The mesh generation over surfaces and regions uses the element removal strategy. The feedback to the parametric space of model entities is used to efficiently resolve some local problems. Meshes of various gradation consisting of well shaped elements are produced. The presented approach is of nearly linear computational complexity for the reasonable mesh density which makes it very competitive for practical use.

The second technique utilizes the tree based approach and is designed for parallel processing. The parallelization strategy is based on the domain decomposition. Two levels of domain decomposition have been considered -- model level and model entity parametric tree level. The discretization of model entities is based on generalized parametric tree data structure and application of templates. A very favourable ratio between the computing and communication has been achieved and also satisfactory load balancing with good speedup have been evidenced. A penalty is paid to outweigh the overall simplicity of the algorithm. The quality of the final mesh depends not only on the mesh size variation but also on the model parameterization. Also the computational performance of the algorithm is dependent on complexity of model parameterization. The restriction on the model topology results in some reduction of the modeling flexibility.

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Daniel Rypl